Question

question 16 of 33 each exterior angle of a regular polygon measures 45°. how many sides does the polygon have? a. 12 b. 8 c. 10 d. 15

Explanation:

Step1: Recall exterior - angle formula

The sum of exterior angles of any polygon is 360°. For a regular polygon with \(n\) sides, each exterior angle \(\theta=\frac{360^{\circ}}{n}\).

Step2: Solve for \(n\)

We know that \(\theta = 45^{\circ}\), so \(n=\frac{360^{\circ}}{\theta}\). Substituting \(\theta = 45^{\circ}\) into the formula, we get \(n=\frac{360}{45}=8\).

Answer:

B. 8